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Axion-like particles may form a network of cosmic strings in the Universe today that can rotate the plane of polarization of cosmic microwave background (CMB) photons. Future CMB observations with improved sensitivity might detect this axion-string-induced birefringence effect, thereby revealing an as-yet unseen constituent of the Universe and offering a new probe of particles and forces that are beyond the Standard Model of Elementary Particle Physics. In this work, we explore how spherical convolutional neural networks (SCNNs) may be used to extract information about the axion string network from simulated birefringence maps. We construct a pipeline to simulate the anisotropic birefringence that would arise from an axion string network, and we train SCNNs to estimate three parameters related to the cosmic string length, the cosmic string abundance, and the axion-photon coupling. Our results demonstrate that neural networks are able to extract information from a birefringence map that is inaccessible with two-point statistics alone (i.e., the angular power spectrum). We also assess the impact of noise on the accuracy of our SCNN estimators, demonstrating that noise at the level anticipated for Stage IV (CMB-S4) measurements would significantly bias parameter estimation for SCNNs trained on noiseless simulated data, and necessitate modeling the noise in the training data., Comment: 23 pages, 7 figures, 4 tables

This document summarizes the discussions which took place during the PITT-PACC Workshop entitled "Non-Standard Cosmological Epochs and Expansion Histories," held in Pittsburgh, Pennsylvania, Sept. 5-7, 2024. Much like the non-standard cosmological epochs that were the subject of these discussions, the format of this workshop was also non-standard. Rather than consisting of a series of talks from participants, with each person presenting their own work, this workshop was instead organized around free-form discussion blocks, with each centered on a different overall theme and guided by a different set of Discussion Leaders. This document is not intended to serve as a comprehensive review of these topics, but rather as an informal record of the discussions that took place during the workshop, in the hope that the content and free-flowing spirit of these discussions may inspire new ideas and research directions., Comment: 33 pages, LaTeX, 2 figures

We provide a framework for numerically computing the effects of free-streaming in scalar fields produced after inflation. First, we provide a detailed prescription for setting up initial conditions in the field. This prescription allows us to specify the power spectra of the fields (peaked on subhorizon length scales and without a homogeneous field mode), and importantly, also correctly reproduces the behaviour of density perturbations on large length scales consistent with superhorizon adiabatic perturbations. We then evolve the fields using a spatially inhomogeneous Klein-Gordon equation, including the effects of expansion and radiation-sourced metric perturbations. We show how gravity enhances, and how free streaming erases the initially adiabatic density perturbations of the field, revealing more of the underlying, non-evolving, white-noise isocurvature density contrast. Furthermore, we explore the effect of non-gravitational self-interactions of the field, including oscillon formation, on the suppression dynamics. As part of this paper, we make our code, ${\sf{Cosmic-Fields-Lite}}$ (${\sf{CFL}}$), publicly available. For observationally accessible signatures, our work is particularly relevant for structure formation in light/ultralight dark matter fields., Comment: v3: added footnote 5. v2: added references, fixed typos. v1: 38 pages + references and appendices, 13 figures. See https://github.com/hypermania/Cosmic-Fields-Lite for our code $\sf{Cosmic-Fields-Lite}$ and https://www.youtube.com/playlist?list=PLecJrnvnk5c7Iaqi-Wq7xvqk1Msgxn5pk for videos of simulation results

(Ultra)light spin-$1$ particles -- dark photons -- can constitute all of dark matter (DM) and have beyond Standard Model couplings. This can lead to a coherent, oscillatory signature in terrestrial detectors that depends on the coupling strength. We provide a signal analysis and statistical framework for inferring the properties of such DM by taking into account (i) the stochastic and (ii) the vector nature of the underlying field, along with (iii) the effects due to the Earth's rotation. Owing to equipartition, on time scales shorter than the coherence time the DM field vector typically traces out a fixed ellipse. Taking this ellipse and the rotation of the Earth into account, we highlight a distinctive three-peak signal in Fourier space that can be used to constrain DM coupling strengths. Accounting for all three peaks, we derive latitude-independent constraints on such DM couplings, unlike those stemming from single-peak studies. We apply our framework to the search for ultralight $B - L$ DM using optomechanical sensors, demonstrating the ability to delve into previously unprobed regions of this DM candidate's parameter space., Comment: 23 pages, 9 figures, and 5 appendices. Compared to v2, added 1 figure. Also, for a movie of the vector field behavior based on simulations, visit https://www.youtube.com/watch?v=bbw6yFRLS7s

Artificial monopoles have been engineered in various systems, yet there has been no systematic study of the singular vector potentials associated with the monopole field. We show that the Dirac string, the line singularity of the vector potential, can be engineered, manipulated, and made manifest in a spinor atomic condensate. We elucidate the connection among spin, orbital degrees of freedom, and the artificial gauge, and show that there exists a mapping between the vortex filament and the Dirac string. We also devise a proposal where preparing initial spin states with relevant symmetries can result in different vortex patterns, revealing an underlying correspondence between the internal spin states and the spherical vortex structures. Such a mapping also leads to a new way of constructing spherical Landau levels, and monopole harmonics. Our observation provides insights into the behavior of quantum matter possessing internal symmetries in curved spaces., Comment: 5 pages + 5 figures + 5 appendices. In comparison with the previous version, we have (1) added supplementary material as appendices, and (2) made some minor revisions in the main text. Also, a simulation video for creating two artificial Dirac Strings with a mixed spin-1 state, is available at https://youtu.be/PCQGMqd-DfQ

Massive vector fields can form spatially localized, non-relativistic, stationary field configurations supported by gravitational interactions. The ground state configurations (p-solitons/vector solitons/dark photon stars/polarized Proca stars) have a time-dependent vector field pointing in the same spatial direction throughout the configuration at any instant of time, can carry macroscopic amounts of spin angular momentum, and are spherically symmetric and monotonic in the energy density. In this paper, we include general relativistic effects, and numerically investigate the stability of compact polarized Proca stars (linear and circularly polarized) and compare them to hedgehog-like field configurations (with radially pointing field directions). Starting with approximate field profiles of such stars, we evolve the system numerically using 3+1 dimensional numerical simulations in general relativity. We find that these initial conditions lead to stable configurations. However, at sufficiently large initial compactness, they can collapse to black holes. We find that the initial compactness that leads to black hole formation is higher for circularly polarized stars (which carry macroscopic spin angular momentum), compared to linearly polarized ones, which in turn is higher than that for hedgehog configurations., Comment: 10 pages, 6 figures

We provide an algorithm for evolving general spin-$s$ Gross-Pitaevskii / non-linear Schr\"odinger systems carrying a variety of interactions, where the $2s+1$ components of the `spinor' field represent the different spin-multiplicity states. We consider many nonrelativistic interactions up to quartic order in the Schr\"odinger field (both short and long-range, and spin-dependent and spin-independent interactions), including explicit spin-orbit couplings. The algorithm allows for spatially varying external and/or self-generated vector potentials that couple to the spin density of the field. Our work can be used for scenarios ranging from laboratory systems such as spinor Bose-Einstein condensates (BECs), to cosmological/astrophysical systems such as self-interacting bosonic dark matter. As examples, we provide results for two different setups of spin-$1$ BECs that employ a varying magnetic field and spin-orbit coupling, respectively, and also collisions of spin-$1$ solitons in dark matter. Our symplectic algorithm is second-order accurate in time, and is extensible to the known higher-order accurate methods., Comment: 13 pages, 3 figures, 2 appendices

We study the nonlinear effects of minimally coupled, massless, cosmological scalar fields on the cosmic microwave background (CMB). These fields can exhibit post-recombination parametric resonance and subsequent nonlinear evolution leading to novel contributions to the gravitational potential. We compute the resulting contributions to the CMB temperature anisotropies through the time-variation of the gravitational potential (i.e., the integrated Sachs-Wolfe (ISW) effect). We find that fields that constitute 5% of the total energy density and become dynamical at $z_c \simeq 10^{4}$ can produce marginally observable ISW signals at multipoles $\ell \simeq 2000$. Fields that become dynamical at earlier times and/or have initial displacements at a flatter part of their potential, produce ISW contributions that are significantly larger and at higher multipoles. We calculate these dynamics and the resulting evolution of gravitational perturbations using analytic estimates alongside detailed nonlinear lattice simulations, which couple scalar fields and cosmological fluids to a perturbed metric. Finally, we discuss the possibility of detecting these features with future high-resolution CMB observations., Comment: 12 pages, 6 figures, comments welcome; v2 minor typo corrected

Using wave kinetics, we estimate the emergence time-scale of gravitating Bose-Einstein condensates/Bose stars in the kinetic regime for a general multicomponent Schr\"{o}dinger-Poisson (SP) system. We identify some effects of the diffusion and friction pieces in the wave-kinetic Boltzmann equation (at leading order in perturbation theory) and provide estimates for the kinetic nucleation rate of condensates. We test our analysis using full $3+1$ dimensional simulations of multicomponent SP system. With an eye towards applications to multicomponent dark matter, we investigate two general cases in detail. First is a massive spin-$s$ field with $N=2s+1$ components (scalar $s=0$, vector $s=1$ and tensor $s=2$). We find that for a democratic population of different components, the condensation time-scale is $\tau_{(s)}\approx \tau_0\times N$, where $\tau_0$ is the condensation time scale for the scalar case. Second is the case of two scalars with different boson masses. In this case, we map-out how the condensation time depends on the ratios of their average mass densities and boson masses, revealing competition and assistance between components, and a guide towards which component condenses first. For instance, with $m_1 < m_2$ and not too disparate mass densities, we verify that the time scale of condensation of the first species quickly becomes independent of $m_2/m_1$, whereas for equal average number densities, the emergence time scale decreases with increasing $m_2/m_1$., Comment: 8 pages + 3 appendices, 5 figures. Videos from simulations are available at https://mustafa-amin.com/home/multicomponent-dark-matter. In comparison with the previous version, we have (1) added more references; (2) provide clarifications in Appendix A and account for an additional factor of 2 in the wave kinetic equation

Wave-like dark matter made of spin-1 particles (dark photons) is expected to form ground state clumps called "vector solitons", which can have different polarizations. In this work, we consider the interaction of dark photons with photons, expressed as dimension-6 operators, and study the electromagnetic radiation that arises from an isolated vector soliton due to parametric resonant amplification of the ambient electromagnetic field. We characterize the directional dependence and polarization of the outgoing radiation, which depends on the operator as well as the polarization state of the underlying vector soliton. We discuss the implications of this radiation for the stability of solitons and as a possible channel for detecting mergers of vector solitons through astrophysical observations., Comment: 30 pages, 2 figures. V2: Updated towards version published in JCAP

We investigate cosmological structure formation in Fuzzy Dark Matter (FDM) with an attractive self-interaction (SI) with numerical simulations. Such a SI would arise if the FDM boson were an ultra-light axion, which has a strong CP symmetry-breaking scale (decay constant). Although weak, the attractive SI may be strong enough to counteract the quantum 'pressure' and alter structure formation. We find in our simulations that the SI can enhance small-scale structure formation, and soliton cores above a critical mass undergo a phase transition, transforming from dilute to dense solitons., Comment: 10 pages, 3 figures, submitted to mnras

We argue that there is a lower bound of order $10^{-19}$ eV on dark matter mass if it is produced after inflation via a process with finite correlation length. We rely on non-detection of free-streaming suppression and white-noise enhancement of density perturbations as the observational inputs., Comment: v3: compared to v2, change in the definition of the suppression scale due to free streaming, 10^(-19) eV bound not affected, but stronger bounds in particular explicit examples weakened

We provide an algorithm and a publicly available code to numerically evolve multicomponent Schr\"{o}dinger-Poisson (SP) systems with a SO($n$) symmetry, including attractive or repulsive self-interactions in addition to gravity. Focusing on the case where the SP system represents the non-relativistic limit of a massive vector field, non-gravitational self-interactions (in particular spin-spin interactions) introduce complexities related to mass and spin conservation which are not present in purely gravitational systems. We address them with an analytical solution for the `kick' step in the algorithm, where we are able to decouple the multicomponent system completely. Equipped with this analytical solution, the full field evolution is second order accurate, preserves spin and mass to machine precision, and is reversible. Our algorithm allows for an expanding universe relevant for cosmology, and the inclusion of external potentials relevant for laboratory settings., Comment: 18 pages, 3 figures, 4 appendices. A python code based on our algorithm in provided at, https://github.com/mudit-jain90/i-SPin . Animations of the numerical simulation results can be found at, https://www.youtube.com/watch?v=KUbVtULiBtE . (Added discussions of another algorithm, along with its generalization.)

The Koopman-von Neumann (KvN) theory is one where the dynamical momentum is not canonically conjugate to position, i.e., position and momentum are deconjugated. From this point of view, we show that the KvN theory arises from quantum mechanics, extracting classical equations of motion from quantum ones. However, preserving the canonical structure of the theory requires introducing ``auxiliary'' canonical conjugates to position and momentum. We show that using the KvN formulation to study the interaction between quantum and classical systems forces the auxiliary variables to take on a physical role. While giving rise to classical behaviour, the KvN theory might be more than classical., Comment: 6 pages

Cosmological and astrophysical observations currently provide the only robust, positive evidence for dark matter. Cosmic probes of dark matter, which seek to determine the fundamental properties of dark matter through observations of the cosmos, have emerged as a promising means to reveal the nature of dark matter. This report summarizes the current status and future potential of cosmic probes to inform our understanding of the fundamental nature of dark matter in the coming decade., Comment: Report of the CF3 Topical Group for Snowmass 2021; 35 pages, 10 figures, many references. V3 updates Fig 3-2 and the author list

Axion-like particles (ALPs) can form a network of cosmic strings and domain walls that survives after recombination and leads to anisotropic birefringence of the cosmic microwave background (CMB). In addition to studying cosmic strings, we clarify and emphasize how the formation of ALP-field domain walls impacts the cosmic birefringence signal; these observations provide a unique way of probing ALPs with masses in the range $3H_0 \lesssim m_a \lesssim 3H_{\rm cmb}$. Using measurements of CMB birefringence from several telescopes, we find no evidence for axion-defect-induced anisotropic birefringence of the CMB. We extract constraints on the model parameters that include the ALP mass $m_a$, ALP-photon coupling $\mathcal{A} \propto g_{a\gamma\gamma} f_a$, the domain wall number $N_{\rm dw}$, and parameters characterizing the abundance and size of defects in the string-wall network. Considering also recent evidence for isotropic CMB birefringence, we find it difficult to accommodate this with the non-detection of anisotropic birefringence under the assumption that the signal is generated by an ALP defect network., Comment: 20 pages + 3 appendices, 14 figures, 3 tables

We investigate the differences in the small-scale structure of vector dark matter (VDM) and scalar dark matter (SDM) using 3+1 dimensional simulations of single/multicomponent Schr\"{o}dinger-Poisson system. We find that the amount of wave interference, core-to-halo mass ratio (and its scatter), spin of the core, as well as the shape of the central regions of dark matter halos can distinguish VDM and SDM. Starting with a collection of idealized halos (self-gravitating solitons) as an initial condition, we show that the system dynamically evolves to an approximately spherically symmetric configuration that has a core surrounded by a halo of interference patterns in the mass density. In the vector case, the central soliton in less dense and has a smoother transition to an $r^{-3}$ tail compared to the scalar case. As compared to SDM, wave interference in VDM is $\sim 1/\sqrt{3}$ times smaller, resulting in fewer low and high density regions, and more diffuse granules in the halo. The ratio of VDM core mass to the total halo mass is lower than that in SDM, with a steeper dependence on the total energy of the system and a slightly larger scatter. Finally, we also initiate a study of the evolution of intrinsic spin angular momentum in the VDM case. We see a positive correlation between the total intrinsic spin in the simulation and the spin of the final central core, with significant scatter. We see large intrinsic spin in the core being possible even with vanishing amounts total angular momentum in the initial conditions (at least instantaneously). Our results point towards the possibility of distinguishing VDM from SDM using astrophysical and terrestrial observations., Comment: v3: 19 pages, 7 figures and an appendix. References added + minor changes to match published version

Over the past few decades, astronomical and cosmological data sets firmly established the existence of physics beyond the Standard Model of particle physics by providing strong evidence for the existence of dark matter, dark energy, and non-zero neutrino mass. In addition, the generation of primordial perturbations most likely also relies on physics beyond the Standard Model of particle physics. Theory work, ranging from models of the early universe in string theory that that led to novel phenomenological predictions to the development of effective field theories to large-scale cosmological simulations that include the physics of galaxy evolution, has played a key role in analyzing and interpreting these data sets and in suggesting novel paths forward to isolate the origins of this new physics. Over the next decade, even more sensitive surveys are beginning to take data and are being planned. In this white paper, we describe key areas of the theory program that will be needed to optimize the physics return on investment from these new observational opportunities., Comment: Contribution to Snowmass 2021

Many well-motivated extensions of the Standard Model predict the existence of new light species that may have been produced in the early universe. Prominent examples include axions, sterile neutrinos, gravitinos, dark photons, and more. The gravitational influence of light relics leaves imprints in the cosmic microwave background fluctuations, the large-scale structure of the universe and the primordial element abundances. In this paper, we detail the physics of cosmological light relics, and describe how measurements of their relic density and mass serve as probes of physics beyond the Standard Model. A measurement of the light relic density at the precision of upcoming cosmological surveys will point the way toward new physics or severely constrain the range of viable extensions to the Standard Model., Comment: Contribution to Snowmass 2021. 59 pages, 12 figures

This Snowmass 2021 White Paper describes the Cosmic Microwave Background Stage 4 project CMB-S4, which is designed to cross critical thresholds in our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. We provide an overview of the science case, the technical design, and project plan., Comment: Contribution to Snowmass 2021. arXiv admin note: substantial text overlap with arXiv:1908.01062, arXiv:1907.04473

The non-linear process of cosmic structure formation produces gravitationally bound overdensities of dark matter known as halos. The abundances, density profiles, ellipticities, and spins of these halos can be tied to the underlying fundamental particle physics that governs dark matter at microscopic scales. Thus, macroscopic measurements of dark matter halos offer a unique opportunity to determine the underlying properties of dark matter across the vast landscape of dark matter theories. This white paper summarizes the ongoing rapid development of theoretical and experimental methods, as well as new opportunities, to use dark matter halo measurements as a pillar of dark matter physics., Comment: White paper submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). 88 pages, 9 figures. Comments welcome

Oscillons are spatially localized, time-periodic and long-lived configurations that were primarily proposed in scalar field theories with attractive self-interactions. In this letter, we demonstrate that oscillons also exist in the low-energy effective theory of an interacting massive (real) vector field. We provide two types of vector oscillons with vanishing orbital angular momentum, and approximately spherically symmetric energy density, but not field configurations. These are: (1) "directional" oscillons (linearly polarized), with vanishing total intrinsic spin, and (2) "spinning" oscillons (circularly polarized) with a macroscopic instrinsic spin equal to $\hbar\times$ number of particles in the oscillon. In contrast to the case with only gravitational interactions, the two oscillons have different energy at a fixed particle number even in the nonrelativistic limit. By carrying out relativistic $3+1$d simulations, we show that these oscillons can be long-lived (compared to the oscillation time for the fields), and can arise from a range of Gaussian initial spatial profiles. These considerations make vector oscillons potentially relevant during the early universe and in dark photon dark matter, with novel phenomenology related to their polarization., Comment: v2: 5 pages, 3 figures with appendices. Updates to appendix A and motivation, matches published version

We first show that the effective non-relativistic theory of gravitationally interacting, massive integer-spin fields (spin-$0$, $1$, and $2$ in particular) is described by a $2s+1$ component Schr\"{o}dinger-Poisson action, where $s$ is the spin of the field. We then construct $s+1$ distinct, gravitationally supported solitons in this non-relativistic theory from identically polarized plane waves. Such solitons are extremally polarized, with macroscopically large spin, but no orbital angular momentum. These $s+1$ solitons form a basis set, out of which partially polarized solitons can be constructed. All such solitons are ground states, have a spherically symmetric energy density but not field configurations. We discuss how solitons in higher-spin fields can be distinguished from scalar solitons, and potential gravitational and non-gravitational probes of them., Comment: 14 + 2 pages, 5 figures, added more references, submitted to PRD

Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure quantum/classical bracket when acting on pure quantum/classical variables. Any hybrid bracket obeying these natural requirements will produce the same dynamics for pure classical or quantum variables, given a hybrid Hamiltonian. Backreaction is manifested in the evolution of a nonvanishing commutator between classical variables. The more massive the classical system is, the less it is affected by backreaction. Interestingly, we show that while pure variables evolve to violate the pure canonical relations, they always obey the hybrid canonical relations. The dynamics of hybrid variables, on the other hand, is shown to require a fully specified and consistent hybrid bracket, otherwise evolution cannot be defined., Comment: 6 pages, 1 figure

Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schr\"{o}dinger-Poisson (SP) equations in a cosmological context. In this paper, starting from the nonlinear and fully relativistic Klein-Gordon-Einstein (KGE) equations in an expanding universe, we provide a systematic framework for deriving the SP equations, as well as relativistic corrections to them, by integrating out `fast modes' and including nonlinear metric and matter contributions. We provide explicit equations for the leading-order relativistic corrections, which provide insight into deviations from the SP equations as the system approaches the relativistic regime. Upon including the leading-order corrections, our equations are applicable beyond the domain of validity of the SP system, and are simpler to use than the full KGE case in some contexts. As a concrete application, we calculate the mass-radius relationship of solitons in scalar dark matter and accurately capture the deviations of this relationship from the SP system towards the KGE one., Comment: 20 pages, 5 figures, plus appendices

We investigate the production of photons from coherently oscillating, spatially localized clumps of axionic fields (oscillons and axion stars) in the presence of external electromagnetic fields. We delineate different qualitative behaviour of the photon luminosity in terms of an effective dimensionless coupling parameter constructed out of the axion-photon coupling, and field amplitude, oscillation frequency and radius of the axion star. For small values of this dimensionless coupling, we provide a general analytic formula for the dipole radiation field and the photon luminosity per solid angle, including a strong dependence on the radius of the configuration. For moderate to large coupling, we report on a non-monotonic behavior of the luminosity with the coupling strength in the presence of external magnetic fields. After an initial rise in luminosity with the coupling strength, we see a suppression (by an order of magnitude or more compared to the dipole radiation approximation) at moderately large coupling. At sufficiently large coupling, we find a transition to a regime of exponential growth of the luminosity due to parametric resonance. We carry out 3+1 dimensional lattice simulations of axion electrodynamics, at small and large coupling, including non-perturbative effects of parametric resonance as well as backreaction effects when necessary. We also discuss medium (plasma) effects that lead to resonant axion to photon conversion, relevance of the coherence of the soliton, and implications of our results in astrophysical and cosmological settings., Comment: 12 figures, 28 pages + 1 Appendix

The polarization of Cosmic Microwave Background (CMB) photons is rotated as they pass through (ultralight-) axion string loops. Studying this birefringence can reveal valuable information about the axion-photon coupling and the structure of the string network. We develop an approximate analytic formalism and identify a kernel function that can be used to calculate the two-point correlation function for CMB birefringence induced by an arbitrary axion string network. Using this formalism, we evaluate the birefringence signal for some simple loop distributions (including scaling and network collapse). We find that the angular correlation function has a characteristic angular scale set by $\theta_\mathrm{min}$, which corresponds to the angular extent of the loops at the time of recombination. This results in a peak in the birefringence power spectrum around $\ell_p \sim 1/\theta_\mathrm{min}$. An additional scale, controlled by the axion's mass, is introduced if the network collapses before today., Comment: 31 pages + appendices; 9 figures. v2: updated towards the version published in JCAP (added limits from ACTPol n SPTPol in power spectrum figures; added more references)

We investigate the bursts of electromagnetic and scalar radiation resulting from the collision, and merger of oscillons made from axion-like particles using 3+1 dimensional lattice simulations of the coupled axion-gauge field system. The radiation into photons is suppressed before the merger. However, it becomes the dominant source of energy loss after the merger if a resonance condition is satisfied. Conversely, the radiation in scalar waves is dominant during initial merger phase but suppressed after the merger. The backreaction of scalar and electromagnetic radiation is included in our simulations. We evolve the system long enough to see that the resonant photon production extracts a significant fraction of the initial axion energy, and again falls out of the resonance condition. We provide a parametric understanding of the time, and energy scales involved in the process and discuss observational prospects of detecting the electromagnetic signal., Comment: 21 pages, 6 figures + 4 pages of Appendix (v2, updated references and minor changes in text)

We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. Introducing a hybrid composition product, we show that such a bracket is the commutator of that product. From this we see that the hybrid bracket will obey the Jacobi identity and the Leibniz rule provided the composition product is associative. This suggests that the set of hybrid variables belonging to an associative subalgebra with the composition product will have consistent quantum-classical dynamics. This restricts the class of allowed quantum-classical interaction Hamiltonians. Furthermore, we show that pure quantum or classical variables can interact in a consistent framework, unaffected by no-go theorems in the literature or the restrictions for hybrid variables. In the proposed scheme, quantum backreaction appears as quantum-dependent terms in the classical equations of motion., Comment: Published in Physical Review A, minor revisions to v3, 11 pages

CMB-S4---the next-generation ground-based cosmic microwave background (CMB) experiment---is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semi-analytic projection tool, targeted explicitly towards optimizing constraints on the tensor-to-scalar ratio, $r$, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2--3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments given a desired scientific goal. To form a closed-loop process, we couple this semi-analytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for $r > 0.003$ at greater than $5\sigma$, or, in the absence of a detection, of reaching an upper limit of $r < 0.001$ at $95\%$ CL., Comment: 24 pages, 8 figures, 9 tables, submitted to ApJ. arXiv admin note: text overlap with arXiv:1907.04473

It is commonly assumed that the energy density of the Universe was dominated by radiation between reheating after inflation and the onset of matter domination 54,000 years later. While the abundance of light elements indicates that the Universe was radiation dominated during Big Bang Nucleosynthesis (BBN), there is scant evidence that the Universe was radiation dominated prior to BBN. It is therefore possible that the cosmological history was more complicated, with deviations from the standard radiation domination during the earliest epochs. Indeed, several interesting proposals regarding various topics such as the generation of dark matter, matter-antimatter asymmetry, gravitational waves, primordial black holes, or microhalos during a nonstandard expansion phase have been recently made. In this paper, we review various possible causes and consequences of deviations from radiation domination in the early Universe - taking place either before or after BBN - and the constraints on them, as they have been discussed in the literature during the recent years., Comment: 67 pages, 18 figures. v2: Discussion and references added. Accepted for publication in The Open Journal of Astrophysics

Oscillons are extremely long-lived, spatially-localized field configurations in real-valued scalar field theories that slowly lose energy via radiation of scalar waves. Before their eventual demise, oscillons can pass through (one or more) exceptionally stable field configurations where their decay rate is highly suppressed. We provide an improved calculation of the non-trivial behavior of the decay rates, and lifetimes of oscillons. In particular, our calculation correctly captures the existence (or absence) of the exceptionally long-lived states for large amplitude oscillons in a broad class of potentials, including non-polynomial potentials that flatten at large field values. The key underlying reason for the improved (by many orders of magnitude in some cases) calculation is the systematic inclusion of a spacetime-dependent effective mass term in the equation describing the radiation emitted by oscillons (in addition to a source term). Our results for the exceptionally stable configurations, decay rates, and lifetime of large amplitude oscillons (in some cases $\gtrsim 10^8$ oscillations) in such flattened potentials might be relevant for cosmological applications., Comment: v2: 27 pages, 7 figures. References added, added short discussion on cosine potentials

We calculate the curvature power spectrum sourced by spectator fields that are excited repeatedly and non-adiabatically during inflation. In the absence of detailed information of the nature of spectator field interactions, we consider an ensemble of models with intervals between the repeated interactions and interaction strengths drawn from simple probabilistic distributions. We show that the curvature power spectra of each member of the ensemble shows rich structure with many features, and there is a large variability between different realizations of the same ensemble. Such features can be probed by the cosmic microwave background (CMB) and large scale structure observations. They can also have implications for primordial black hole formation and CMB spectral distortions. The geometric random walk behavior of the spectator field allows us to calculate the ensemble-averaged power spectrum of curvature perturbations semi-analytically. For sufficiently large stochastic sourcing, the ensemble-averaged power spectrum shows a scale dependence arising from the time spent by modes outside the horizon during the period of particle production, in spite of there being no preferred scale in the underlying model. We find that the magnitude of the ensemble-averaged power spectrum overestimates the typical power spectra in the ensemble because the ensemble distribution of the power spectra is highly non-Gaussian with fat tails., Comment: 68 pages, 23 figures

We present a new numerical algorithm and code, ${\sf GFiRe}$, for solving the non-linear evolution of Abelian gauge fields coupled to complex scalar fields in homogeneous and isotropic spacetimes. We adopt a hybrid approach to solving the system: the spatial derivatives are discretized using standard Lattice Gauge Field Theory techniques, whereas the time evolution of the fields and scale factor is implemented with explicit, composite, symplectic integrators. An important property of our compound algorithm is that the discretized Gauss constraint is respected exactly, regardless of the order of the symplectic integrator. This remains true even when the background expansion is computed "self-consistently"; that is, when the expansion history is computed using spatial averaged components of the energy momentum tensor in the simulation volume. Hence, our code can also be used in cases where the fields dominate the energy density of the universe, for example, during reheating after inflation. We test the algorithm in scenarios of reheating where the inflaton is a complex scalar field with a potential $\propto(2|\varphi|^2-v^2)^2$ and is coupled to an Abelian gauge field. Tracing the evolution of the system through complex dynamics (including resonant excitation of fields, backreaction, formation of solitons, and changes in the equation of state) in a self-consistently expanding universe, we find the energy conservation violation ($<10^{-4}$) to be very stable and the Gauss constraint violation ($<10^{-6}$) to be dominated by differencing noise., Comment: 35 pages, 13 figures; minor changes, accepted for publication in JCAP

Bose-Einstein Condensate Dark Matter (BECDM; also known as Fuzzy Dark Matter) is motivated by fundamental physics and has recently received significant attention as a serious alternative to the established Cold Dark Matter (CDM) model. We perform cosmological simulations of BECDM gravitationally coupled to baryons and investigate structure formation at high redshifts ($z \gtrsim 5$) for a boson mass $m=2.5\cdot 10^{-22}~{\rm eV}$, exploring the dynamical effects of its wavelike nature on the cosmic web and the formation of first galaxies. Our BECDM simulations are directly compared to CDM as well as to simulations where the dynamical quantum potential is ignored and only the initial suppression of the power spectrum is considered -- a Warm Dark Matter-like ("WDM") model often used as a proxy for BECDM. Our simulations confirm that "WDM" is a good approximation to BECDM on large cosmological scales even in the presence of the baryonic feedback. Similarities also exist on small scales, with primordial star formation happening both in isolated haloes and continuously along cosmic filaments; the latter effect is not present in CDM. Global star formation and metal enrichment in these first galaxies are delayed in BECDM/"WDM" compared to the CDM case: in BECDM/"WDM" first stars form at $z\sim 13$/$13.5$ while in CDM star formation starts at $z\sim 35$. The signature of BECDM interference, not present in "WDM", is seen in the evolved dark matter power spectrum: although the small scale structure is initially suppressed, power on kpc scales is added at lower redshifts. Our simulations lay the groundwork for realistic simulations of galaxy formation in BECDM., Comment: 19 pages, 12 figures, submitted to MNRAS

In hierarchical models of structure formation, the first galaxies form in low-mass dark matter potential wells, probing the behavior of dark matter on kiloparsec (kpc) scales. Even though these objects are below the detection threshold of current telescopes, future missions will open an observational window into this emergent world. In this Letter we investigate how the first galaxies are assembled in a `fuzzy' dark matter (FDM) cosmology where dark matter is an ultralight $\sim 10^{-22}$~eV boson and the primordial stars are expected to form along dense dark matter filaments. Using a first-of-its-kind cosmological hydrodynamical simulation, we explore the interplay between baryonic physics and unique wavelike features inherent to FDM. In our simulation, the dark matter filaments show coherent interference patterns on the boson de Broglie scale and develop cylindrical soliton-like cores which are unstable under gravity and collapse into kpc-scale spherical solitons. Features of the dark matter distribution are largely unaffected by the baryonic feedback. On the contrary, the distributions of gas and stars, which do form along the entire filament, exhibit central cores imprinted by dark matter -- a smoking gun signature of FDM., Comment: 6 pages, 2 figures, accepted to Phys. Rev. Lett

We present a detailed investigation of a sub-dominant oscillating scalar field ('early dark energy', EDE) in the context of resolving the Hubble tension. Consistent with earlier work, but without relying on fluid approximations, we find that a scalar field frozen due to Hubble friction until ${\rm log}_{10}(z_c)\sim3.5$, reaching $\rho_{\rm EDE}(z_c)/\rho_{\rm tot}\sim10$%, and diluting faster than matter afterwards can bring cosmic microwave background (CMB), baryonic acoustic oscillations, supernovae luminosity distances, and the late-time estimate of the Hubble constant from the SH0ES collaboration into agreement. A scalar field potential which scales as $V(\phi) \propto \phi^{2n}$ with $2\lesssim n\lesssim 3.4$ around the minimum is preferred at the 68% confidence level, and the {\em Planck} polarization places additional constraints on the dynamics of perturbations in the scalar field. In particular, the data prefers a potential which flattens at large field displacements. An MCMC analysis of mock data shows that the next-generation CMB observations (i.e., CMB-S4) can unambiguously detect the presence of the EDE at very high significance. This projected sensitivity to the EDE dynamics is mainly driven by improved measurements of the $E$-mode polarization. We also explore new observational signatures of EDE scalar field dynamics: (i) We find that depending on the strength of the tensor-to-scalar ratio, the presence of the EDE might imply the existence of isocurvature perturbations in the CMB. (ii) We show that a strikingly rapid, scale-dependent growth of EDE field perturbations can result from parametric resonance driven by the anharmonic oscillating field for $n\approx 2$. This instability and ensuing potentially nonlinear, spatially inhomogenoues, dynamics may provide unique signatures of this scenario., Comment: 26 pages, 22 figures, comments welcome

We provide an overview of the science case, instrument configuration and project plan for the next-generation ground-based cosmic microwave background experiment CMB-S4, for consideration by the 2020 Decadal Survey., Comment: Project White Paper submitted to the 2020 Decadal Survey, 10 pages plus references. arXiv admin note: substantial text overlap with arXiv:1907.04473

Development of the hardware, data analysis, and simulation techniques for large compact radio arrays dedicated to mapping the 21 cm line of neutral hydrogen gas has proven to be more difficult than imagined twenty years ago when such telescopes were first proposed. Despite tremendous technical and methodological advances, there are several outstanding questions on how to optimally calibrate and analyze such data. On the positive side, it has become clear that the outstanding issues are purely technical in nature and can be solved with sufficient development activity. Such activity will enable science across redshifts, from early galaxy evolution in the pre-reionization era to dark energy evolution at low redshift., Comment: 10 pages + references, 2 figures, 1 table; APC white paper submitted to the Astro2020 decadal survey. arXiv admin note: text overlap with arXiv:1810.09572

In this white paper, we discuss the prospects for characterizing and identifying dark matter using gravitational waves, covering a wide range of dark matter candidate types and signals. We argue that present and upcoming gravitational wave probes offer unprecedented opportunities for unraveling the nature of dark matter and we identify the most urgent challenges and open problems with the aim of encouraging a strong community effort at the interface between these two exciting fields of research., Comment: 17 pages, 2 figures. Comments welcome. v2: Added references and minor corrections

The axion is a hypothetical, well-motivated dark-matter particle whose existence would explain the lack of charge-parity violation in the strong interaction. In addition to this original motivation, an `axiverse' of ultra-light axions (ULAs) with masses $10^{-33}\,{\rm eV}\lesssim m_{\rm a}\lesssim 10^{-10}\,{\rm eV}$ also emerges from string theory. Depending on the mass, such a ULA contributes to the dark-matter density, or alternatively, behaves like dark energy. At these masses, ULAs' classical wave-like properties are astronomically manifested, potentially mitigating observational tensions within the $\Lambda$CDM paradigm on local-group scales. ULAs also provide signatures on small scales such as suppression of structure, interference patterns and solitons to distinguish them from heavier dark matter candidates. Through their gravitational imprint, ULAs in the presently allowed parameter space furnish a host of observational tests to target in the next decade, altering standard predictions for microwave background anisotropies, galaxy clustering, Lyman-$\alpha$ absorption by neutral hydrogen along quasar sightlines, pulsar timing, and the black-hole mass spectrum., Comment: 5 pages, 1 figure, Astro2020 Decadal Survey science white paper

The hot dense environment of the early universe is known to have produced large numbers of baryons, photons, and neutrinos. These extreme conditions may have also produced other long-lived species, including new light particles (such as axions or sterile neutrinos) or gravitational waves. The gravitational effects of any such light relics can be observed through their unique imprint in the cosmic microwave background (CMB), the large-scale structure, and the primordial light element abundances, and are important in determining the initial conditions of the universe. We argue that future cosmological observations, in particular improved maps of the CMB on small angular scales, can be orders of magnitude more sensitive for probing the thermal history of the early universe than current experiments. These observations offer a unique and broad discovery space for new physics in the dark sector and beyond, even when its effects would not be visible in terrestrial experiments or in astrophysical environments. A detection of an excess light relic abundance would be a clear indication of new physics and would provide the first direct information about the universe between the times of reheating and neutrino decoupling one second later., Comment: 5 pages + references; 1 figure; science white paper submitted to the Astro2020 decadal survey

The next generation of instruments designed to measure the polarization of the cosmic microwave background (CMB) will provide a historic opportunity to open the gravitational wave window to the primordial Universe. Through high sensitivity searches for primordial gravitational waves, and tighter limits on the energy released in processes like phase transitions, the CMB polarization data of the next decade has the potential to transform our understanding of the laws of physics underlying the formation of the Universe., Comment: 5 pages + references; Submitted to the Astro2020 call for science white papers

There are two big questions cosmologists would like to answer -- How does the Universe work, and what are its origin and destiny? A long wavelength gravitational wave detector -- with million km interferometer arms, achievable only from space -- gives a unique opportunity to address both of these questions. A sensitive, mHz frequency observatory could use the inspiral and merger of massive black hole binaries as standard sirens, extending our ability to characterize the expansion history of the Universe from the onset of dark energy-domination out to a redshift z ~ 10. A low-frequency detector, furthermore, offers the best chance for discovery of exotic gravitational wave sources, including a primordial stochastic background, that could reveal clues to the origin of our Universe., Comment: White Paper submitted on March 8, 2019 to Astro2020 (2020 Decadal Survey on Astronomy and Astrophysics)

Our current understanding of the Universe is established through the pristine measurements of structure in the cosmic microwave background (CMB) and the distribution and shapes of galaxies tracing the large scale structure (LSS) of the Universe. One key ingredient that underlies cosmological observables is that the field that sources the observed structure is assumed to be initially Gaussian with high precision. Nevertheless, a minimal deviation from Gaussianityis perhaps the most robust theoretical prediction of models that explain the observed Universe; itis necessarily present even in the simplest scenarios. In addition, most inflationary models produce far higher levels of non-Gaussianity. Since non-Gaussianity directly probes the dynamics in the early Universe, a detection would present a monumental discovery in cosmology, providing clues about physics at energy scales as high as the GUT scale., Comment: 5 pages + references; Submitted to the Astro2020 call for science white papers. This version: fixed author list

We explore non-adiabatic particle production in a de Sitter universe for a scalar spectator field, by allowing the effective mass $m^2(t)$ of this field and the cosmic time interval between non-adiabatic events to vary stochastically. Two main scenarios are considered depending on the (non-stochastic) mass $M$ of the spectator field: the conformal case with $M^2=2H^2$, and the case of a massless field. We make use of the transfer matrix formalism to parametrize the evolution of the system in terms of the "occupation number", and two phases associated with the transfer matrix; these are used to construct the evolution of the spectator field. Assuming short-time interactions approximated by Dirac-delta functions, we numerically track the change of these parameters and the field in all regimes: sub- and super-horizon with weak and strong scattering. In all cases a log-normally distributed field amplitude is observed, and the logarithm of the field amplitude approximately satisfies the properties of a Wiener process outside the horizon. We derive a Fokker-Planck equation for the evolution of the transfer matrix parameters, which allows us to calculate analytically non-trivial distributions and moments in the weak-scattering limit., Comment: 80 pages, 44 figures

We investigate the formation, gravitational clustering and interactions of solitons in a self-interacting, non-relativistic scalar field in an expanding universe. Rapid formation of large number of solitons is driven by attractive self-interactions of the field, whereas the slower clustering of solitons is driven by gravitational forces. Driven closer together by gravity, we see a rich plethora of dynamics in the soliton "gas" including mergers, scatterings and formation of soliton binaries. The numerical simulations are complemented by analytic calculations and estimates of (i) the relevant instability length and time scales, (ii) individual soliton profiles and their stability, (iii) number density of produced solitons, and (iv) the two point correlation function of soliton positions as evidence for gravitational clustering., Comment: v3: 17 pages, 8 Figures. References added, extended discussion in the appendices, minor changes in the text. Matches version accepted for publication in PRD

We study the scalar and tensor perturbations generated by the fragmentation of the inflaton condensate into oscillons or transients after inflation, using nonlinear classical lattice simulations. Without including the backreaction of metric perturbations, we find that the magnitude of scalar metric perturbations never exceeds a few $\times 10^{-3}$, whereas the maximal strength of the gravitational wave signal today is $\mathcal{O}(10^{-9})$ for standard post-inflationary expansion histories. We provide parameter scalings for the $\alpha$-attractor models of inflation, which can be easily applied to other models. We also discuss the likelihood of primordial black hole formation, as well as conditions under which the gravitational wave signal can be at observationally interesting frequencies and amplitudes. Finally, we provide an upper bound on the frequency of the peak of the gravitational wave signal, which applies to all preheating scenarios., Comment: 18 pages, 8 figures

At the end of inflation, the inflaton field decays into an initially nonthermal population of relativistic particles which eventually thermalize. We consider the production of dark matter from this relativistic plasma, focusing on the prethermal phase. We find that for a production cross section $\sigma(E)\sim E^n$ with $n> 2$, the present dark matter abundance is produced during the prethermal phase of its progenitors. For $n\le 2$, entropy production during reheating makes the nonthermal contribution to the present dark matter abundance subdominant compared to that produced thermally. As specific examples, we verify that the nonthermal contribution is irrelevant for gravitino production in low scale supersymmetric models ($n=0$) and is dominant for gravitino production in high scale supersymmetry models ($n=6$)., Comment: 12 pages, 4 figures

It has been recently suggested that oscillons produced in the early universe from certain asymmetric potentials continue to emit gravitational waves for a number of $e$-folds of expansion after their formation, leading to potentially detectable gravitational wave signals. We revisit this claim by conducting a convergence study using graphics processing unit (GPU)-accelerated lattice simulations and show that numerical errors accumulated with time are significant in low-resolution scenarios, or in scenarios where the run-time causes the resolution to drop below the relevant scales in the problem. Our study determines that the dominant, growing high frequency peak of the gravitational wave signals in the fiducial "hill-top model" in [arXiv:1607.01314] is a numerical artifact. This finding prompts the need for a more careful analysis of the numerical validity of other similar results related to gravitational waves from oscillon dynamics., Comment: v2: 6 pages, 2 figures; matches PRD version